Chapter 3: Q12. (page 111)

If x and $2 x - 15$ represent the measures of the acute angles of a right triangle, find the value of x.

Short Answer

Expert verified

The value of x is 35.

Step by step solution

Step 1. Apply the definition of right-angled triangle.

A right-angled triangle is a type of triangle in which measure of one of its angles is 90 degrees.

Step 2. Apply an angle sum theorem.

The sum measure of all angles of a triangle is 180°.

According to given condition,

$\begin{matrix} x + 2 x - 15 + 90 = 180 \\ 3 x - 15 + 90 = 180 \\ 3 x = 180 - 75 \\ = 105 \end{matrix}$

Step 3. Description of step.

Divide each side of the obtained equation in step 2 by 3 to find the value of x.

$\begin{matrix} \frac{3 x}{3} = \frac{105}{3} \\ x = 35 \end{matrix}$

Therefore, the value of x is 35.

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If x and $2 x - 15$ represent the measures of the acute angles of a right triangle, find the value of x.

Short Answer

Step by step solution

Step 1. Apply the definition of right-angled triangle.

Step 2. Apply an angle sum theorem.

Step 3. Description of step.

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If x and2x-15 represent the measures of the acute angles of a right triangle, find the value of x.

Short Answer

Step by step solution

Step 1. Apply the definition of right-angled triangle.

Step 2. Apply an angle sum theorem.

Step 3. Description of step.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Geometry

Theoretical and Mathematical Physics

Probability and Statistics

Decision Maths

Logic and Functions

Calculus

Study anywhere. Anytime. Across all devices.

If x and $2 x - 15$ represent the measures of the acute angles of a right triangle, find the value of x.